Problem: $\lim_{x\to \frac{\pi}{3}}\sec(x)=?$ Choose 1 answer: Choose 1 answer: (Choice A) A $2$ (Choice B) B $\sqrt{2}$ (Choice C) C $\dfrac{1}{2}$ (Choice D) D The limit doesn't exist.
Explanation: $\sec(x)$ is continuous on all points in its domain. Therefore, if $x=\dfrac{\pi}{3}$ is within the domain of $\sec(x)$, we can find $\lim_{x\to \frac{\pi}{3}}\sec(x)$ by direct substitution. $x=\dfrac{\pi}{3}$ is indeed in the domain of $\sec(x)$ : $\begin{aligned} \sec\left(\dfrac{\pi}{3}\right)&=\dfrac{1}{\cos\left(\dfrac{\pi}{3}\right)} \\\\ &=\dfrac{1}{\left( \dfrac{1}{2} \right)} \\\\ &=2 \end{aligned}$ $\lim_{x\to \frac{\pi}{3}}\sec(x)=2$